Consider the problem of modeling hysteresis for finite-state random walks using higher-order Markov chains. This Letter introduces a Bayesian framework to determine, from data, the number of prior states of recent history upon which a trajectory is statistically dependent. The general recommendation is to use leave-one-out cross validation, using an easily-computable formula that is provided in closed form. Importantly, Bayes factors using flat model priors are biased in favor of too-complex a model (more hysteresis) when a large amount of data is present and the Akaike information criterion (AIC) is biased in favor of too-sparse a model (less hysteresis) when few data are present.

翻译：考虑使用高阶马可夫链制成的限定州随机行走的歇斯底里模型的问题。本信引入了拜伊西亚框架,以便从数据中确定在统计上取决于轨迹的近代历史的先期状态的数量。一般建议是使用一种容易计算、但以封闭形式提供的公式,对放假一次交叉验证。重要的是,使用平板模型前缀的贝伊因因素偏向于一种过于复杂的模型(更多的歇斯底里),因为存在大量数据,而Akaike信息标准偏向于一种过于粗略的模型(无歇斯底里),而数据很少存在。